A157701 Decimal expansion of 2*(14*sigma+5)/625 where sigma = sqrt(5)*log(golden ratio).

0, 6, 4, 2, 0, 5, 8, 0, 1, 3, 8, 7, 9, 6, 8, 4, 5, 2, 3, 5, 5, 6, 1, 6, 5, 2, 2, 0, 9, 0, 4, 6, 7, 8, 0, 7, 6, 4, 7, 5, 5, 1, 9, 1, 6, 4, 4, 4, 5, 1, 2, 4, 4, 1, 3, 3, 2, 7, 8, 4, 6, 8, 3, 6, 4, 7, 1, 6, 6, 8, 5, 6, 1, 3, 1, 6, 4, 6, 7, 7, 9, 6, 7, 2, 4, 8, 6, 9, 0, 9, 6, 4, 6, 0, 8, 8, 6, 3, 5, 0, 0, 5, 5, 0, 9

Offset

0,2

Comments

The factor 28 in the Lehmer paper has been corrected to 14.

Equals sum_{n=1..infinity} (-1)^n*n^3/binomial(2n,n).

Links

Table of n, a(n) for n=0..104.

D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.

R. J. Mathar, Corrigenda to "Interesting series involving...", arXiv:0905.0215

Index entries for transcendental numbers

Formula

Equals 2*(14*A002163*A002390+5)/625 .

Example

0.064205801387968452355..

Maple

2/625*(14*sqrt(5)*log((1+sqrt(5))/2)+5) ;

Mathematica

Join[{0}, RealDigits[2*(14*Sqrt[5]*Log[GoldenRatio]+5)/625, 10, 120][[1]]] (* Harvey P. Dale, Mar 13 2015 *)

Prog

(PARI) 2*(14*sqrt(5)*log((sqrt(5)+1)/2)+5)/625 \\ Charles R Greathouse IV, May 15 2019

Crossrefs

Cf. A145434, A145433.

Sequence in context: A117254 A211022 A021613 * A193076 A073449 A134300

Adjacent sequences: A157698 A157699 A157700 * A157702 A157703 A157704

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 04 2009

Status

approved